Combining eq.tP-2+4,eq.Q-def,eq.E-tlambda2k, it is apparent that the first polynomials have the form eq.Q-2+4. As \(\widetilde{P}_{2r-1,n}=0\)  and the expected value of the relevant \(\widetilde{\lambda }\)  and its powers do not provide terms of orders \(n^{-(2r-1)/2}\)  for any \(r\in \mathbb {N}\) , also \(Q_{2r-1}=0\)  for all \(r\in \mathbb {N}\) .
The approximating polynomials \(Q_r\)  can be directly calculated by Chung's method [1]}, [2]}, by the \(\delta \) -method or by the smooth function model which are both explained in detail in [3]}.
